The great abstract ideas (considered directly and not merely in tacit use) which have dominated the science were due to them - namely, ratio, **irrationality**, continuity, the point, the straight line, the plane.

In 1761 he proved the **irrationality** of 7r; a simpler proof was given somewhat later by Legendre.

In one of the notes Legendre gives a proof of the **irrationality** of 7r.

This property is referred to as the "**irrationality** of dispersion."

The **irrationality** of dispersion is well illustrated by C.Christiansen's experiments on the dispersive properties of white powders.

Lambert, 1 " read before the Berlin Academy in 1761, in which he demonstrated the **irrationality** of 7r.

The general test of **irrationality** which he established is that, if a l a, a, be an interminate continued fraction, a l, a2,

This want of proportion in the dispersion for different regions of the spectrum is called the "**irrationality** of dispersion"; and it is as a direct consequence of this **irrationality**, that there exists a secondary spectrum or residual colour dispersion, showing itself at the focus of all such telescopes, and roughly in proportion to their size.

These glasses, however, still hold the field, although glasses are now produced whose **irrationality** of dispersion has been reduced to a very slight amount.

Moreover the greater depths of the curves (or "curvature powers") in itself neutralize more or less the advantages obtained from the reduced **irrationality** of dispersion.